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Analysis Mathematica, 1987
The Hilbert transform of f is given by the formula \(Hf(x)=(1/\pi)\int^{\infty}_{-\infty}(x-t)^{-1}f(t)dt,\) where the integral is taken in the principal value sense. Let \(L^*\) be the collection of all function f such that \((1+| t|)^{-1}f(t)\) is integrable on (-\(\infty,\infty)\), and let \(L^ p_{\alpha}(R)\) be the class of function f for which \(\
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The Hilbert transform of f is given by the formula \(Hf(x)=(1/\pi)\int^{\infty}_{-\infty}(x-t)^{-1}f(t)dt,\) where the integral is taken in the principal value sense. Let \(L^*\) be the collection of all function f such that \((1+| t|)^{-1}f(t)\) is integrable on (-\(\infty,\infty)\), and let \(L^ p_{\alpha}(R)\) be the class of function f for which \(\
openaire +2 more sources
2010
Publisher Summary This chapter focuses on a generalized way of treating narrow-banded processes from mathematical and physical points of view using the Hilbert transform. The methods described are not limited to narrow-banded processes but work perfectly well for broad-banded spectra as well. When working with theoretical or experimental wave trains,
openaire +2 more sources
Publisher Summary This chapter focuses on a generalized way of treating narrow-banded processes from mathematical and physical points of view using the Hilbert transform. The methods described are not limited to narrow-banded processes but work perfectly well for broad-banded spectra as well. When working with theoretical or experimental wave trains,
openaire +2 more sources
2009
The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader.
openaire +1 more source
The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader.
openaire +1 more source
On an Inequality for the Hilbert Transform
Journal of the London Mathematical Society, 1977openaire +1 more source
A Generalisation of the Hilbert Transform
Journal of the London Mathematical Society, 1965openaire +1 more source
ON THE FINITE HILBERT TRANSFORMATION
The Quarterly Journal of Mathematics, 1951openaire +1 more source
On a Modification of the Hilbert Transform
Journal of the London Mathematical Society, 1967openaire +1 more source
Hilbert transform in vibration analysis
Mechanical Systems and Signal Processing, 2011Michael Feldman
exaly